biquads

A biquad is a second-order filter section used in analog and digital signal processing. It serves as a building block for infinite-impulse-response IIR filters, and is designed to realize specific frequency responses with a small number of coefficients. In digital implementations, a biquad section is typically implemented with two delays.

In digital form, the transfer function is H(z) = (b0 + b1 z^-1 + b2 z^-2) / (1 + a1 z^-1 + a2 z^-2). The corresponding difference equation is y[n] = b0 x[n] + b1 x[n-1] + b2 x[n-2] - a1 y[n-1] - a2 y[n-2].

Biquads realize common filter types such as low-pass, high-pass, band-pass, notch, all-pass and shelving filters. Multiple biquad sections can be cascaded to form higher-order filters with improved numerical stability and localized pole-zero placement.

In analog form, biquads refer to second-order active filter circuits (for example, multiple-feedback or state-variable implementations) built around operational amplifiers. In digital form, numerical stability is aided by careful coefficient scaling and choosing a representation that minimizes quantization error.

Source design methods include deriving coefs from analog prototypes (Butterworth, Chebyshev, Bessel) via bilinear transform or using direct-design equations for specific Q, center frequency, and gain. They are widely used in audio processing, musical effects, and communications.